JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If one of the roots of the equation \[{{x}^{2}}+ax+b=0\] and \[{{x}^{2}}+bx+a=0\] is coincident, then the numerical value of \[(a+b)\] is                  [IIT 1986; RPET 1992; EAMCET 2002]

    A) 0

    B) - 1

    C) 2

    D) 5

    Correct Answer: B

    Solution :

    If \[\alpha \] is the coincident root, then \[{{\alpha }^{2}}+a\alpha +b=0\]and \[{{\alpha }^{2}}+b\alpha +a=0\] Þ \[\frac{{{\alpha }^{2}}}{{{a}^{2}}-{{b}^{2}}}=\frac{\alpha }{b-a}=\frac{1}{b-a}\] Þ\[{{\alpha }^{2}}=-(a+b);\alpha =1\,\,\Rightarrow -(a+b)=1\]Þ \[(a+b)=-1\].


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